---
title: Complex Differentiation
description: Complex differentiation extends the concept of the derivative to functions of complex variables. Learners will understand holomorphicity, apply the Cauchy-Riemann equations, and analyze the properties of analytic functions.
category: mathematics
subcategory: complex-analysis
difficulty: beginner, intermediate, advanced
url: /subject/complex-differentiation
---

# Complex Differentiation

Complex differentiation extends the concept of the derivative to functions of complex variables. Learners will understand holomorphicity, apply the Cauchy-Riemann equations, and analyze the properties of analytic functions.

## Available Resources

4 Courses • 1 Websites

## Courses

### 1. Complex Analysis

Learn complex differentiation with Prof. Thangavelu's engaging Complex Analysis course. Master key concepts and problem-solving techniques!

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLbMVogVj5nJS_i8vfVWJG16mPcoEKMuWT

### 2. Complex Analysis

Learn complex differentiation with Dr. Linda Green's comprehensive Complex Analysis course. Explore key concepts and techniques!

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLVMgvCDIRy1wzJcFNGw7t4tehgzhFtBpm

### 3. Complex Variables with Applications (MIT 18.04)

**Author:** Jeremy Orloff

Complex analytic functions and their applications: Cauchy's theorem and integral formula, Taylor and Laurent series, residues for evaluating hard integrals, harmonic functions, conformal maps, two-dimensional fluid flow, and Laplace and Fourier transforms. Provides 14 lecture note files plus problem sets and exams with solutions.

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://ocw.mit.edu/courses/18-04-complex-variables-with-applications-spring-2018/

**Tags:** complex-analysis, analytic-functions, residue-theorem, laurent-series, conformal-mapping

### 4. Introduction to Complex Analysis

**Author:** Petra Bonfert-Taylor

Wesleyan University course on complex analysis covering complex numbers, analytic functions, conformal mappings, Möbius transformations, contour integration, Cauchy's theorem, power and Laurent series, and residues. Learners finish able to evaluate contour integrals and analyze complex-differentiable functions.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/complex-analysis

**Tags:** complex-analysis, analytic-functions, conformal-mapping, contour-integration, residue-theorem

## Websites

### 1. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

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